Areas of simple 2D shapes

Learning Objective:

• we are learning to use comparison and calculation to find, understand and use formulae to give the area of a range of simple 2D shapes.
• By the end of this unit/lesson you will be able to calculate the:
  • area of a rectangle
  • area of a square
  • area of a parallelogram
  • area of a right-angled triangle
  • area of a non-right-triangle
  • area of a kite
  • area of a trapezium
• area of compound shapes and area of circles and parts of circles form separate lessons

Investing:

• The history of mathematics is rich with problems involving finding the area and volume of shapes. The Moscow papyrus (~1850 B.C) and the Rhynd papyrus (~1650 B.C.) are ancient Egyptian texts full of ‍‍problems concerning areas and volumes ‍‍and show some of the earliest examples of proto-algebra (the beginnings of algebra). As the audio below tells us, knowledge of such calculation was considered to be an essential requirement for enty into the civil service of the day and would guarantee you a good career!

The Rhynd Papyrus circa 1650 B.C.

• You can download and listen to a short discussion about the history and importance of the Rhynd papyrus from the BBC's series A History of the World in 100 Objects

• Today finding areas might be useful to you in all sorts of practical situations:
• This skill leads to...
• A 'free gift' with this skill is that we can now also...
• This could help you if you want to work in...

Preparing:

• Are we ready? Can you already... ?
• Let's be sure you can...
• Before you start you need to know:
• You will have a deeper understanding if you also know:

Discovering:

• Can you figure it out yourself from these examples?

transforming areas tool.exe

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• 986 KB

APP how do you know (areas).pdf

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• 1 MB

APP how do you know (areas) sample student work.pdf

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• 2 MB

• Try to predict the next one aloud or on a mini-whiteboard.
• Investigate...

Modeling:

• Here are some examples of people getting it right:
• Here are some examples of people getting it wrong in typical ways:
• Here are some more examples. Did they get it right or wrong? Explain how you know!

Discussing:

• What would this one be? Tell your learning partner. Convince them you're right.
• Explain how you know.
• How would you explain this to someone who was new to it?

Explaining:

• One way to do this is...
• Another approach might be...
• A useful shortcut is to...
• This works because...
• It doesn't work when...
• An exception is...
• Watch out for...
• A common mistake is...
• You can check your result by...
• We can prove this works by...

Practicing:

• Some straightforward examples.
• Some harder examples.
• Comparing areas in disected squares - scaffolded with hints from math4teaching.com:

• This leads us to a lovely lesson designed as part of the Standards Unit:

the main activity - open the pdf below or download from the national STEM centre (click this picture)

standards unit ss3 - dissecting a square.pdf

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• 157 KB

• Some non-examples to spot and some mixed questions with redundant, insufficient or contradictory data.
• You can demonstrate fluency by at least...

Sharing:

• A web page or wiki I have created to explain this can be found at...
• A presentation I have created and rehearsed looks like...
• A poster I have drawn or model I have made can be found...

Assessing:

• Check you've mastered this skill by...
• Show you understand by explaining...
• Prove you're an expert in... by...

Developing:

• Next we could learn...
• This leads to...
• Now try...